PRIVILEGE, POWER AND PERFORMATIVITY: THE ETHICS OF ...



PRIVILEGE, POWER AND PERFORMATIVITY: THE ETHICS OF MATHEMATICS IN SOCIETY AND EDUCATION Paul ErnestUniversity of Exeter, UKp.ernest @ ex.ac.ukABSTRACTThe undoubted benefits and intrinsic virtues of mathematics should not blind us to potential collateral damage as the huge juggernaut of mathematics rolls over education and society towards a reshaped future. Because of its great power and influence across the whole of society we need to undertake an ethical audit. This paper conducts an ethical critique that considers four interrelated aspects of mathematics in education and society and their negative impacts. 1. The overvaluation of mathematics and the effects this power has in maintaining privileges. 2. The powerful negative impacts of mathematical studies have on many individual learners. 3. Visible but problematic applications of mathematics within society that are shielded from criticism because mathematics continues to be viewed as neutral. 4. The profound and performative effects of the hidden applications of mathematics that reformat society and change our everyday lives but remain unchecked in every sense. Most of the paper is devoted to revealing these damaging effects. The solutions proposed are for ethical awareness to be fostered in mathematical study at all levels, as well as challenging the widespread stereotype of mathematics as ethically neutral. IntroductionA central problem for ethics in mathematics and its teaching is that the goodness of mathematics is taken for granted. It is widely and uncritically assumed not only to be wholly beneficial but also to be beyond any ethical responsibility. In this paper I question this assumption and undertake an ethical audit of mathematics for education and society. This is a critical analysis of both the good and the harm mathematics causes, both individually and socially. Of course mathematics is very important and because of its immense power plays a vital role in many aspects of modern life. However, because of this power and ubiquity, an ethical light needs to be shone on its uses and applications to check if, and if so, where they are harmful. Any harmful applications of mathematics, and I shall suggest several, need to be uncovered, held to account and mitigated. An awareness of the ethical dimensions of mathematics needs to be raised within the community of mathematicians, who need to develop a sense of their social responsibilities. Mathematicians need to see that they share responsibility for helping to solve the urgent social and environmental problems the world now faces. To this end the ethics of mathematics needs to be addressed throughout education; foregrounding its role in understanding as well as solving the world’s most urgent social and environmental problems. Only through education can the involvement of mathematics in the urgent problems facing the world be forgrounded, as well as showing the central part that mathematics has to play in solving these problems. Why is mathematics widely assumed to be such an untrammelled good? The reasons are several. First of all, mathematics is undoubtedly very powerful, and its applications are ubiquitous. It underpins science, technology, computing, business, government, health, education, finance and other aspects of human functioning. Second, educational qualifications in mathematics are a passport allowing entry to many jobs, access to higher education, and a doorway to many of the most fulfilling and rewarding professions. Third, mathematics is a central element in human culture of great beauty and conferring great insights into reason and the world. In addition, I, the present author, and my colleagues in the research community are mathematical insiders. We belong to a group including mathematicians, mathematics educators, mathematics teachers, mathematics-related professionals and others who have specialised in mathematics. For insiders like as us, mathematics is a love object: endlessly fascinating, attractive and beautiful. We see it as meaningful, useful, powerful and also as an avenue to personal success. As insiders we are deeply invested in mathematics, we see the world through the lens of mathematics; so not surprisingly we are strong advocates for the high valuation and prestige of mathematics in education and society. It would never occur to most mathematicians to question the value of mathematics, let alone to question its ethics; to ask if mathematics can possibly be harmful or damaging to individuals or society. Given the perceived objectivity, aloofness and neutrality of mathematics if there is any damage to individuals that results from the encounter with mathematics it is usually attributed to their own faults or weakness. Any harm caused to society is usually attributed to bad individuals misusing or making unethical applications of mathematics. Mathematics itself, this view insists, cannot be responsible for negative impacts on individuals or society.For mathematics outsiders, that is the general public, there is a wide diversity of views. Many of the public also love or at least like mathematics, as we insiders do, and are fascinated and enjoy recreational mathematics and popular presentations of the subject. But for a significant minority of the public at the very least, mathematics is seen to be cold, hard, unforgiving, masculine, meaningless, joyless, rejecting or frightening (Buerk 1982, Buxton 1981, Maxwell 1989). For these persons, it is something to be avoided, or at best tolerated as a necessary evil when it has to be used or negotiated in study or everyday life (Evans 2000). For a significant minority mathematics is seen as an obstacle to educational and career advancement and is feared and, where possible, skipped or circumvented. For many, success in mathematics is understood as being based on the inherited ability of a few special others, the ‘mathematically gifted’, and is not related to the effort expended in school (Mutodi and Ngirande 2014, Sisk et al. 2018).Making an Ethical evaluation of mathematics Why would one want to make an ethical evaluation of mathematics? Precisely because of its importance. Mathematics is perhaps the most universally taught subject in schools around the world. Furthermore, schooling is an intrinsically ethical enterprise in that it is intended to benefit both students and society. It is also a socially accountable activity, so all elements of education need to be justified in terms of the full range of benefits they confer, and the limits to such benefits. Thus mathematics in education needs a justification, and one that is critically balanced and does not prejudge the outcome because of conventional historical assumptions or the views of insiders or ideologically slanted interest groups. Elsewhere I have argued that even the aims of mathematics in schooling are controversial and highly contested, with different social groups prioritising distinct and sometimes antagonistic aims and values that favour and benefit certain groups of students over others (Ernest 1991). In conducting an ethical evaluation of mathematics one needs to consider not just good and or harm caused to individuals, but also social good or harm caused by mathematics and the place it is given in society. Such evaluations cannot be wholly general, ‘one-size-fits-all’, for the impact of mathematical experiences vary across different individuals and groups. The social outcomes of mathematics and their benefits differ according to which social groups, activities, institutions and general social functions one considers. What can a critical ethical evaluation of mathematics add to the widespread social justice literature in mathematics education? The latter critiques the social maldistribution of the goods of mathematics. My enquiry also addresses deeper questions about the ethics of mathematics itself, its hidden applications and its overvaluation across society. This encompasses but also goes beyond social justice critiques of mathematics in education and society. An ethical evaluation of mathematicsIn conducting my ethical evaluation I consider four aspects of mathematics. They are interconnected and may overlap to some extent, but listing them separately allows me to emphasise different ways that the applications of mathematics impact on society. Another scholar might come up with a different set of categories, or a different number of them. My list provides me with a structure to address different dimensions of the ethical impact of mathematics within the education system, and more generally across society; sometimes affecting individuals, and often affecting groups of persons or even the whole of society. I should acknowledge that I focus primarily on Western society, on the social issues I experience and see around me as a researcher based in modern Britain, in modern Europe, located in the Anglophone world. How universal these issues are I leave to others to judge. I am sure scholars from the South or East could list further and probably different impacts of mathematics in their education systems and societies. The four aspects of mathematics I consider in my critique are as follows.An acknowledgement of the high, exaggerated even, value given to mathematics and its social outcomes.An examination of the impact of mathematical studies on individual learners.A look at some of the explicit applications of mathematics and their effects on society. Revealing the profound the profound impact of hidden and implicit applications of mathematics on society. In each case I offer some examples of the effects of mathematics to illustrate some of broader ethical issues and problems arising from the place and uses of mathematics in society. The high value given to mathematics in societyMathematics is very highly valued in society. As described above, this is primarily because of its great utility and power. Mathematics is the language and foundation of science, technology and computer science; some of the main theoretical bases of modern social life. Applications of mathematics underpin and structure all large scale social practices including manufacturing, business, trade, finance, government, healthcare, education, the military, public media, information and communication technologies, and so on. The utility and power of mathematics through its applications simply cannot be overestimated. However, there is a fallacious argument that because of this great utility and power the mathematical needs of society are also very great, and that all students must be taught and certified in mathematics to the highest possible level. What are in fact the mathematical needs of society? To answer this question I find it useful to apply Marx’s fundamental distinction between use and exchange value. In economic theory the difference between use value (cost price) and exchange value (sale price) is profit. In education, the difference between use value (actual utility) and exchange value (social or opportunity value) of learning is the educational and social obstacle and filter or conversely the advantage and privilege that is conferred by the learning, or rather by its certification. My claim is that the use value of mathematical studies across the whole of society is limited and the exchange value is exaggerated. For those lacking the cultural capital and backgrounds that offer an advantage in obtaining mathematical certification, for it is never simply a measure of talent, the assessment system in mathematics provides a social obstacle and a filter fabricating a reduction in life chances.According to my analysis the actual mathematical needs of society can be stated as follows. First, everyone needs ‘numeracy plus’ to be functioning critical citizens in a modern democratic society. They need to have mastery of the mathematics underlying their everyday lives including consumer and economic decisions. As functioning modern citizens, they need to be able to interpret and evaluate the uses of mathematics in social, commercial and political claims in published reports, newspaper and other media presentations, advertisements, financial documents, and so on. By ‘numeracy plus’ I mean the content of elementary school mathematics plus some additional knowledge, such as understanding and skill in data representation and processing, spreadsheets and elementary algebra, probability and statistics, ratio and proportion, reasoning and practical problem solving. This should include understanding algorithms, Apps, and big data in principle but not necessarily in detail. Such knowledge needs to empower elementary and everyday applications, rather than being directed exclusively at completing written tasks in external examinations and assessments at 16 years or thereafter. In modern society some mathematical capabilities including the capacity for quantitative reasoning are of course essential. Second, society is highly mathematised with almost all citizens using algorithms in information and communication technologies (ICT), including computers and mobile phones, the media, and so on. These applications are ubiquitous, but as users of Apps and ICT citizens need no deep technical comprehension of the underlying computer logic or mathematics. All most people need for day-to-day functioning is the practical knowledge to operate these devices and Apps. Obviously a highly skilled group of specialists is required to understand the language of mathematics and algorithms to enable the invention, development, evaluation of software and Apps. However, only a tiny minority in highly specialised professions, far less than 1% of the population, need such technical understanding and capabilities.Third, in between the ‘numeracy plus’ capabilities needed by all citizens and the highly technical knowledge for the tiny group of specialists mentioned above, there is the need for additional mathematical knowledge and study. This is for those who need or might need mathematics in further studies at university and in technical and science related professions. These areas and professions include mathematical sciences, physical and biological sciences, experimental psychology, medicine, engineering, accountancy, and so on. This is a small minority which is probably less than 5% of the population. Perhaps one should overestimate this proportion to 10% to create spare capacity; a pool of expertise to enable growth in scientific and technically skilled professions. Of course, in addition, anyone who wants to study mathematics should be enabled and encouraged to do so to whatever level they desire. I certainly do not wish to obstruct the paths of mathematical enthusiasts, I just want to remove the mandatory requirements from those for whom they are an unnecessary obstacle.What this analysis shows is that a majority, or at the very least, a substantial minority do not need mathematical knowledge and skills beyond ‘numeracy plus’. But in modern society the exchange value of mathematics far outweighs its use value. There is a symbolic function of mathematics in which it serves as a social filtration device. Mathematics certification is a critical filter for entry to almost all higher education and professions (Sells 1978). Applicants are required to have successfully completed the study of mathematics to 16 or 18 years of age. Furthermore, this certification is required irrespective of whether the knowledge or skills will be needed in subsequent study or work. If all students gained knowledge and capabilities from studying mathematics, that is, a demonstrable cognitive benefit, it could be argued that it is a worthwhile component of general education. But many young persons are forced to study mathematics involuntarily and a significant number of these experience some degree of failure or incomprehension, suffer loss of self confidence, and develop negative attitudes to mathematics.Furthermore, as a critical filter, mathematics in effect performs a fractional distillation of the population. Those who fail to pass mathematics tests are often denied entry to university, further studies or fulfilling occupations. What is to a large extent an arbitrary test deprives many of their chances for fulfilling studies and rewarding occupations and professions. Historically, up to the 19th century, the classics (Latin and Greek) used to occupy same symbolic role as a critical filter. Entry to the church, governance, diplomacy, the civil service, law, medicine, education, all depended on competency in the classics. Even Shakespeare was mocked during his lifetime as uneducated because he lacked knowledge of the classics. If the job of actor and playwright required formal qualifications, the greatest writer of all time would have been denied entry to his profession.Success in school mathematics is also strongly correlated with the social class background and the socio-economic status of students. Although this is true about success in most academic school subjects, mathematics has a privileged status. High stakes testing in mathematics enacts a fractional distillation which, to a significant extent, is class reproductive. The small number of exceptional mathematicians from any background may be successful in life, although those from poorer backgrounds may have to battle against the odds for recognition. But the net effect of mathematical examinations remains the grading of students into an hierarchy with respect to life chances. This hierarchy correlates with both the social class origins and the socio-economic status of the career destinations of students. So it is not merely raw mathematical talent that is reflected in mathematical achievement. It is also partially but significantly mediated by cultural capital (Bourdieu 1986, Zevenbergen 1998). As mathematics professionals and insiders we are complicit in this over-valuing of mathematics. We gain by not questioning the over-valuing of mathematics in society. We gain more resources, more prestige, and through the privileged place of our subject in schooling. We do not challenge the argument that its ubiquity in society means that all must study abstract mathematics to 16 or 18 years of age. At the same time we accept that not everyone must study the arts, literature, drama, classics, languages, psychology, philosophy, politics, geography, history or computing, despite the contribution these can also make to being active citizens, developing as more rounded persons, and to enjoying the good life. These subjects are surely important for the personal development not to mention the employment of young persons. But we choose to leave these subjects optional. Thus I claim that mathematics is greatly overvalued in modern society, and damagingly so. There is an argument that knowledge and understanding of mathematics are intrinsically valuable, not just as useful skills. At its best, learning mathematics in school offers something unique, beyond its utility. Appreciation of the role of mathematics in everyday life, society, the arts and throughout human culture and history is a valuable outcome of education in its own right (Ernest 2010). Such learning is part of ‘bildung’, forming students’ personalities with regard to their own humanity through education, corresponding to the liberal goal of developing a well-rounded person (Wikipedia 2019). However, I see the ‘numeracy plus’ knowledge of mathematics, embedded in a broad and integrated curriculum, as contributing to this larger goal for education. This should be available to all. My proposals are intended to broaden educational outcomes and opportunities, not to narrow them. The impact of mathematical studies on individualsI have argued that the overvaluation of mathematics has three major immediate social costs. First, there is the unjust exclusion of persons who might well be able to pursue their chosen studies or careers without mathematical certification, but who are excluded by the critical filter of mathematics. Second, the critical filter is class-reproductive, favouring those with cultural capital. This favours the haves over the have nots. Consequently society is denied the benefit of capable people whose backgrounds impede access to the career ladder in many areas. In the UK the notably disadvantaged include white working class males failed by the school system, as well as Afro-Caribbean origin males and members of other ethnic groups, usually from low income backgrounds. Exclusion of any youth group leads to a whole host of future social problems instead of building potentially valuable and fulfilled contributors to society. Third, there is the social cost of negative attitudes to mathematics. Many learners and adults are labelled as mathematics failures, and lack confidence in mathematics and numeracy skills. Some may fear mathematics and thus have reduced opportunities in study and work. Some may have ‘scraped through’, but have negative attitudes because of the personal and emotional costs in passing tests. This happens with some trainee primary school teachers, who are required to teach elementary mathematics to young children, while still doubting their own mathematical ability and efficacy (Ernest 1988). Many other citizens are potentially competent, but are inhibited by negative affect from using their ‘numeracy plus’ skills, to the extent that they have been acquired through elementary schooling, and thus are not fully functioning and participating citizens in modern society. Thus the overvaluation of mathematics, its exaggerated exchange value, leads to the wastage of human power in the workforce, contributes to the reproduction of social inequality, and leads to negative attitudes and reduced self-confidence with regard to mathematics, as well as, for some, reducing full participation in our democratic society. Let us not forget that these negative outcomes will also include reductions in happiness, well-being and life-satisfaction for a significant number of our fellow citizens.An ethical appraisal must surely acknowledge the harm done to some students and citizens by imposing the mandatory study of abstract mathematics beyond its use value because of its inflated exchange value. Surely the education system can accommodate this through a better system of choices, varied mathematical curricula which give students more options? However, in asking this question I am also cognizant of the danger that comes from allowing students to opt out of mathematics prematurely. This risks limiting their future educational and employment possibilities. A balance must be found that maximises student preferences and agency while minimizing the risk of closing off future opportunities and choices. Thus far, in looking at the impact of mathematical studies on individuals I have focussed on negative impacts in terms of failure, exclusion and negative affect. However, a case can be made that success at mathematics can also be ethically problematic. In Ernest (2018) I make the case that the mastery of mathematics necessitates a mode of operational thinking in which the following occurs. Students learn that the meaning of signs and processes is dispensable but that precision in syntax and detail is essential.Success in mathematics requires that linguistic imperatives must be obeyed without question and rules followed precisely in mathematics, constituting a training in obedience.Students acquire the habit of conceptualising situations quantitatively and through simplified mathematical models; and this is strengthened and prioritised across the whole range of lived experience.Reinforcing such thinking is the perception of mathematics as timeless, universal and imbued with absolute certainty; an objective, value-neutral and ethics-free domain of thought. The outcome of all this is that mathematical thinking is constituted as detached instrumental and calculative reasoning. Instrumental reason is the form of action or thought which treats its objects simply as a means and not as ends in themselves. It focuses on the most efficient or most cost-effective means to achieve a specific end, without reflecting on the value of that end, or its ethics. Instrumental reason has been critiqued by a range of philosophers including the critical theorists of the Frankfurt School. Kelman (1973) observes that ethical considerations are eroded when three conditions are present: standardisation, routinisation, and dehumanisation. These are all intrinsic to mathematical thinking so the erasure of ethics when mathematics is applied to the social domain is no surprise. The unchecked instrumentalism of mathematical thinking is potentially harmful, and may well be deleterious to overall human flourishing. Thus even an individual’s success in mathematics is not necessarily an untrammelled good. Being trained to ignore and reject any ethical considerations about the applications of mathematics, and to overlook any collateral damage caused, are potentially harmful or negative outcomes of success in mathematics. Such damage does not reflect an intrinsic weakness of mathematical thinking. It is a defect of human or social thinking and of the application of mathematics viewed purely abstractly. It is potentially rectifiable within a more ethical and thoughtful education system and societal approach to mathematics teaching. Indeed, to some extent, instrumentalist and abstracted modes of reasoning are fully necessary in modern governance. Deploying resources and managing social policies and problems fairly and rationally involves detachment from particular instances. Provided that the background values are humane and directed at human flourishing such actions are intended to, and should do good and cause little or no harm.Teaching abstract mathematical reasoning as value-free can be harmful if the outcome is that appliers of mathematics are led to believe or act as if mathematics and its outcomes are ethics-free. If policy and decision makers only look for the neatest or most profitable mathematical solutions to social problems without looking at the risks, costs or the lived ethical consequences, the results can be harmful. Indeed, where corporations are legally forced to maximise profits and to disregard ethical issues they have been characterised as psychopathic (Bakan 2004). It is the role of good government to regulate corporations and other appliers of mathematics and to protect the interests of its citizens. This opens up the next issue in the ethics of mathematics.Looking at the explicit applications of mathematics in society It is uncontroversial that we need to consider and determine the ethical limits of mathematical applications to ensure the good of society and the safety of all of its members. For example, obtaining private data from millions of unknowing social media users and using algorithms to analyse and use this data to secretly influence their purchasing and voting intentions is unethical and, not surprisingly, also illegal in many countries. An example of a problematic application is that of Credit Default Swaps (CDS), a financial instrument based on emerging markets' sovereign debt. These investments were described as the most dangerous financial products in the markets (BBC News 2013). CDS contributed to the world financial disaster in 2008 and a CDS market can mean that once a government gets in trouble there is no way out. CDS were created using sophisticated mathematics by ‘quants’, quantitative analysts that specialise in applying mathematical and statistical methods to financial and risk management problems. Investments in CDS gave large profits to users and host institutions but helped to trigger the worldwide economic collapse costing banks, governments and citizens trillions of dollars. Although CDS are legal in some countries including the USA, can we say that the invention and use of CDS is unethical? Should the quants behind them have ethical boundaries to discourage them from designing and implementing these risky mathematical applications? Are the banks that bought and sold them culpable? Assuming the financial collapse was unintentional, was it just an accident for which the quants have no ethical responsibility? Jason West (2012) argues that ethics is largely absent from the education of quants, but needs to be included, to try to prevent such catastrophes in future. Echoing this, one of my conclusions in this paper is that ethics should be a necessary adjunct of mathematics teaching at all levels. However, very few mathematicians acknowledge the ethical and social responsibilities of mathematics, even those of applied mathematics. Elsewhere I have argued that the ideology of purism associated with pure mathematics in the modern era contributes to this through repudiating any human interests and ethical values in pure mathematics (Ernest in press). This is supported by the service view of applied mathematics. According to this view applied mathematicians are only the servants of scientists, information technologists and financiers and it exceeds their role to question the ethics of the applications they are asked to develop.It is interesting to contrast these views with parallel views about the social responsibilities of science and scientists. It is widely argued that the Promethean power of modern science and technology warrants an extended ethic of social responsibility. The Russell-Einstein Manifesto called for scientists to take responsibility for developing weapons of mass destruction and urged them to “Remember your humanity, and forget the rest” (Russell and Einstein, 1955). No such call has been heard for mathematics or even for applied mathematics. Examining hidden and implicit applications of mathematics in society The power of mathematics means that it permeates most if not all activities and practices in modern society. Despite its near ubiquity, the role of mathematics in formatting social practices and underpinning social functioning is largely hidden and rarely acknowledged. The ethical impacts of mathematics in society are even more hidden.Given the massive utility and power of mathematics across all sectors of society much of its hidden entanglement in human affairs is for the good, benefiting humankind. However, it cannot simply be taken as an unquestioned assumption that it is always beneficial for everybody. The near invisible and often unnoticed presence of mathematics means there is all the more reason to subject it to an ethical audit. In fact mathematics and its ethical involvement are so well hidden that further theoretical concepts are needed to uncover and describe its effects. These concern the performativity of quantification and measurement, and the fabrication of results, lived truths and objects (Skovsmose and Ravn 2019). When we quantify and measure aspects of social life and reality, we do more than simply describe what is, we modify, shift and redirect social practices. The results of this process are changes, expressed as newly fabricated concepts, objects and activities. A classic example is the IQ measure of intelligence. What the term ‘intelligence’ means is changed by using IQ test scores as a proxy for intelligence. The first criticism of this replacement is that these measures (IQ test results) do not validly capture the full meaning of ‘intelligence’. For example Gould (1981) critiques IQ tests as ‘the mismeasure of man’. He argues that the assumption that worth can be assigned to individuals and groups by measuring intelligence as a single quantity suffers from two deep fallacies. The first is reification, the tendency to convert abstract concepts into entities, such as the intelligence quotient (IQ). The second fallacy Gould identifies is that of ranking, the propensity for ordering complex variation as a linear scale. Both these arguments apply to many measures used in society. Gould forcefully argues that human worth, even only with regard to intelligence, cannot be reduced to a single quantitative measure. Furthermore, he argues, human beings cannot, and for ethical reasons should not, be ranked by a single numerical measure by worth, intelligence or any other quality.Howard Gardner (1983) rejects the model of intelligence as single general ability or measure, and proposes a theory of multiple intelligences with 8 or 9 distinct functional modalities. These include logical-mathematical and verbal-linguistic intelligences, as well as non-academic dimensions such as emotional intelligence. Fineman (2004) offers a cautionary tale of the dangers of assigning a measure to Emotional Intelligence (EQ). The use of IQ test scores as a proxy for intelligence has been socially detrimental. In the UK, IQ scores were a significant part of the 11+ tests for allocating school places to eleven year old children, and through this determining educational futures and life chances. High scorers are admitted to grammar schools (academic schools), with the remaining children allocated to non-academic schools. The poor identification of talents by this simple test blighted the future chances of many capable children, and society lost their potential contributions. Furthermore, higher pass scores were required of girls because there were less places for them at grammar schools. IQ tests were also “used in the United States to deny immigration to Eastern Europeans (who could not speak English) and later to set immigration quotas that discriminated against them, predominantly Jews.” (Allchin 2004; 935). Thus the uses of IQ tests have changed the allocation of resources and life chances and been detrimental to many people.The performativity of IQ scores is also enacted individually. According to labelling theory the social labelling of individuals is often self-fulfilling (Becker 1963). Thus student attitudes and beliefs about IQ, ability and also mathematical ability, including perceptions of own abilities, become internalized, reinforced and realised through their experiences. Others’ opinions of them, particularly labels applied by teachers and parents, can be very influential. The outcome can be self-fulfilling and self-reinforcing cycles. These can take the form of a negative, vicious cycle, the ‘failure cycle’, in which affect, effort and test scores deteriorate, or a positive, virtuous ‘success cycle’ in which affect, effort and test scores are all enhanced (Ernest 2011). In each case, others’ opinions and labels affect students who in believing themselves more (or less) intellectually capable make more (or less) effort and give up more (or less) easily, leading to higher (or lower, respectively) achievement scores in tests. The Pygmalion in the Classroom study (Rosenthal and Jacobson 1968) found that if teacher expectations about student ability are manipulated (high or low) before teaching, those expectations carry over to performances on an IQ test (high or low, respectively). Although the study was severely critiqued, subsequent replications only worked in cases where the teachers were new to the students (Raudenbush 1984). Thus, coupled with social policies, the performativity of IQ measures has led to social and educational practices that are unfair; and through denial of justice, are unethical.These examples illustrate the performativity of measurement. The quantification and measurement of an aspect of social practice creates a new and reified proxy taking on a life of its own, often replacing the original. This newly constructed object is part of larger fabricated system that institutions impose, and through which they remake the social ontology. Measures and concepts are reified into real instruments and systems that regulate society. Policy decisions use this ontology to control and direct citizens, resources and institutions. Thus quantification and measurement play an essential and constitutive role in the exercise of power in society. Mathematics is not just the measure of pre-existing reality, it is constitutive in the making of a new and enacted reality. Mathematics and measurement are entangled in and complicit in the remaking of reality we experience and inhabit. An important part of this process that deserves to be foregrounded is the production of mathematical and computer models that take social measures as inputs. Through the processing encoded in the models output scores are produced that are used to lead to social, fiscal or other policy decisions. Sometimes systems are in place so that social policy decisions for individuals follow automatically from the outputs of the models. But the problem is that “many of these models encode human prejudice, misunderstanding, and bias into the software systems that increasingly managed our lives.” (O’Neil 2016, p. 3). Currently the decisions involved may be in the areas of credit, insurance, social benefits, healthcare, criminal recidivism, court sentencing, child adoption and even child abuse. These are such important aspects of life that the idea that prejudiced, distorted or otherwise flawed models are feeding into or determining people’s life chances and futures is deeply troubling. Where is the ethical scrutiny in this process? It is squeezed out, either by inattention or design. The construction of a measure of some concept or of a model of an aspect of social practice is an epistemological or methodological project. Technical skill, accuracy, precision are the overarching values. At this early point in measure and model fabrication there can be deliberate attempts to slant or even mislead, when measures are used for overtly political purposes (e.g., some government measures of unemployment or poverty, corporate designed Apps to conceal car pollution, such as the VW fraud). For the purposes of measurement many representations will be constructed to meet the appropriate epistemological and methodological standards of the professional community. Virtuous professionals will attempt to make the measures valid, in the sense of accurate and effective. However, even with the greatest skill in the world, there will always be limits to the validity of the representation of any phenomenon, a mismatch between the fuzzy concept image or idea and the operational definition. The applications of such new conceptions imposes new emphases on the social practice, in short they revalue it. When the measures are imposed by institutions and policies to manage, shape and to evaluate social practices the measures become instruments of power to change the practice, they redirect it. This happens even in the most optimistic and honourable situations. But, it would be unrealistic and na?ve to assume that such good intentions and best-in-class outcomes always occur. In modern society, social goods are largely commissioned by governing groups that control material resourcing, whether it be in education, health, manufacturing or other services. Under the neoliberal turn, there is competition among large and small corporate groups to provide goods and services, including public goods. Usually in such cases the lowest bidder is awarded the contract. This contract will specify quantitative targets, the measures taken to represent successful delivery of the social goods. Thus commissioning groups no longer monitor the quality of the social goods provided through professional expertise, but simply check whether the targets are met (Power 1999). This process is subject to two types of moral hazard. First of all, a social good with intrinsic value ceases to be the goal of a practice. Instead a set of quantitative targets are set up as the objectives of the activity. But many social goods involve professional practice, and professionals deploy tacit and contextual knowledge, experience and wisdom in their judgements. These qualities cannot be made fully explicit in the form of targets, let alone as quantitative measures. Thus the moral character of a social good is at risk of dilution or loss, when its successful achievement is measured by attainment targets. The second hazard is that whoever makes a successful bid to deliver the goods or services must minimize costs while maximizing profits. This process means that it is often the cheapest and not the best way to deliver the services that wins out. Bidding and cost minimization means that only just enough effort to attain the targets will be expended. Thus the quality of the goods, and the underlying ethical basis, are at serious risk of compromise.Mathematics in NeoliberalismThe neoliberal perspective is a pervasive modern ideology that appears to be without alternatives. Neoliberalism sees competition as the defining characteristic of human relations. It redefines citizens as consumers, whose democratic choices are best exercised by buying and selling, a process that rewards supplier merit and punishes inefficiency. This perspective regards ‘the market’ as delivering benefits that can never be achieved by government planning. Neoliberalism seeks to maximise market involvement in all business and public affairs, and to minimise state provision of public goods. The language of the market is that of quantified values (exchange values) based on measures, most notably, money. Contrary to the view that neoliberalism represents a form of ‘market fundamentalism’ or simply a revival of nineteenth-century laissez-faire, in fact the key institution of neoliberalism is not a market as such, but particular market-based (or market-derived) forms of economization, calculation, measurement and valuation. (Davies 2017: p. 22)The neoliberal perspective regards the market value of any goods and services to be its objective reality. Other values are disregarded as sentimental, that is subjective attributes that can be ignored by hard-nosed realists. Indeed purists attribute epistemological status to market price, as the only objective social reality. This is performative, in that market price, or any numerical target through which value is determined, becomes constituted as the meaning of any goods, services or social practices. The neoliberal market perspective not only understands the ends of all social and business activities solely in terms of measures, these measures become the realities and meanings of the activities. In this transformation, the mathematisation of all goods and services is essential and inescapable. It also becomes ethics free.Perhaps no field of inquiry has had deeper impact on modern policy thought than economics. Quantification, as much as market fundamentalism, lies at the heart of that impact. (De Mesquita 2019)The British Treasury has codified what Caliskan (2010) terms ‘prosthetic prices’, in contrast to those generated at the moment of market exchange. These are defined through models and other calculative devices, as strategies to dictate how worth is constructed. (Davies 2017). However, the market centred perspective is not limited to the goods, services and practices that can be directly priced, even theoretically, for “all conduct is economic conduct; all spheres of existence are framed and measured by economic terms and metrics, even when those spheres are not directly monetized” (Brown 2015: p. 10). The universal competition underpinning neoliberalism requires universal quantification and comparison. The result is that workers, job-seekers and public services of every kind are subject to a stifling bureaucratic regime of assessment and monitoring, designed to identify the winners (those who meet their targets) and punish the losers (those who don’t). The doctrine that Von Mises (1978) proposed would free us from the bureaucratic nightmare of central planning has instead created one (Monbiot 2017).In the market-led or neoliberal society, all social outcomes are valued and judged in terms of target scores on a linear scale, financial or otherwise quantified, and conceptualized quantitatively. The quality of UK universities are judged in terms of league table scores. Schools and colleges also compete in terms of league table scores. Indeed, the originators of the term, football clubs, are judged literally in terms of football league table scores. All sports are competitively judged in terms of scores. Even individuals within education are judged by their scores on linear scales for entry to university, for achievement at the completion of university study, and for entry to employment or to continued education after study. International comparisons rate whole countries’ education systems in terms of single scores, such as the PISA scores for numeracy. As Gorur (2016, p. 598) points out “PISA is much more than a ‘representation’ … it is not descriptive but performative; and, finally, ‘seeing like PISA’ is bringing about deep-rooted changes, and it is likely that the effects will be very long-term”. Mathematics plays an essential and inescapable part in this process, for without quantification and measures the transformation of social reality could not take place. Thus mathematics is deeply entangled, perhaps even complicit in this social transformation, the neoliberalisation and marketisation of social goods and their provision.First of all, the mathematisation and ascription of measures to services and social practices simplifies their measurement and redirects the targets to what is measurable as well as what suits the bias of the providers and commissioners. The measures of success, scores on targets which if not arbitrary are highly contingent on the measures adopted, become reified into free floating goods in themselves. This process also removes trust from professionals and self-regulated social practices (Power 1999). Second, because of the conceptual changes the measurement discipline feeds back and alters the social activities and goods as realized in practice. The adoption of these measures is performative, changing ideas of success and refocusing social activities towards achieving the imposed measures as opposed to providing the goods that were the original ends. Foucault (1980) describes this a ‘regime of truth’ in which the powerful redefine reality.Third, the re-engineered understanding of the world alters people’s and institutions’ envisioning of the future and their potential lines of action, development and even political possibilities and futures. Personal foregrounds (Skovsmose 2014) and political freedoms are at risk and will often be redirected or narrowed. Beer (2016: 6, original italics) describes this process of performativity and its outcomes succinctly as the “relations that exist between measurement, circulation, and possibility.” These are important social changes, with powerful and potentially immense ethical implications. Individual mindsets and social reshapings take place without explicit ethical awareness, consideration, or discussion in what are vaunted as democratic societies. My purpose here is not to make direct ethical judgements about neoliberalism and the centrality of the market model versus social cooperation and state provision. My purpose here is to point out the centrality of measures and mathematisation in the neoliberal market perspective and the work they do in reformatting personal and social practices without any ethical consideration. As we have seen the use of these measures is performative in changing understandings and social policy, action and reality as well as possible futures available to individuals and society. These changes are being made without public awareness or outcry, let alone democratic control. Marjanovic et al. (2018) term the many negative consequences of just part of this ‘algorithmic pollution’, but I thing a more appropriate term is ‘algorithmic injustice’.A burgeoning new subfield is emerging, the sociology of measurement, quantification and calculation, which is recording, analysing and theorising these developments (Beer 2016, Berman and Hirschman 2018, Mennicken & Espeland 2019). However, there is little recognition of it in the mathematics community. Foucault’s (1976,1980) work pioneered the analysis of the regulative, controlling state and its apparatuses of governmentality. Although he placed mathematics among the conceptual systems of surveillance and control he did not single it out, especially. However, since Foucault’s death with burgeoning of information and communication technologies mathematics has enabled the ideology of measurement intrinsic to neoliberalism, and to most modern governments and corporations, to permeate every channel and crevice of modern life. Just as digitised streams of electromagnetic information permeate our bodies and places from every direction, so too mathematised data flows to and from virtually every human activity and social practice as they are subjected to the electronic gaze of measurement. These metrics and data flows not only monitor and regulate all the activities that they permeate. In a cycle that includes understanding of practices, control of practices and reform of practices the mathematisation entangled in social reality changes it. The forces or measurement and mathematics are performative, radically reshaping and restructuring human practices and social reality, and even the futures and possibilities we can imagine. As mathematicians we have a special duty to acknowledge and identify these applications of our discipline and to scrutinise them ethically. As democratic citizens we share with all other citizens the duty to take responsibility for the direction that social policy is taking, and be cognizant of its social justice and ethical implications. `ConclusionBecause of its great power and influence across the whole of society we need to make an ethical audit of mathematics. The undoubted benefits and intrinsic virtues of mathematics should not blind us to potential collateral damage as the huge juggernaut of mathematics rolls over education and society towards a reshaped future. The overvaluation of mathematics in modern society causes harm, including the role of mathematics as a critical filter in society. Its exchange value far exceeds its use value and thus it serves as an impediment to equal opportunities for all, favouring those with cultural capital. In addition, the personal impact of learning mathematics on learners’ thinking and life chances can be negative for many students, especially but not exclusively those labelled as innumerate or mathematical failures. For those fortunate enough to be successful, the universal training in mathematics leads to an instrumental style of thinking that can be damaging when applied beyond mathematics to social and human issues, through stripping out the ethical and personal dimensions of understanding and actions. This is one of the big problems concerning the role and place of mathematics in society, and intentionally or not, it helps reconfigure social practices through quantification into unanticipated new forms. The applications of mathematics in society often have very powerful ethical implications as recent scandals over algorithm and data misuse have shown, but mathematics rests firmly on an objectivist and neutral ideology and shrugs off any questions of responsibility. In examining the hidden and unquestioned applications in society a truly dark side of mathematics is revealed; the role of metrics and algorithms in re-envisioning social practices, in reformatting social policy and thus social reality, and in reshaping and curtailing the possible futures for everybody. One obstacle to raising awareness of these problems, let alone trying to solve them, are the philosophical and ideological positions that state mathematics is neutral, value-free, and bears no responsibility for any of its applications. Despite the widespread movements concerned with the social responsibility of science, almost no parallels for mathematics exist. However the ethically questionable uses of mathematics are widespread all around us. Mathematical algorithms have been used to mine personal data of millions of citizens for commercial advantage and political influence. Money, written and spoken in the language of mathematics, is the tool for the circulation and distribution of wealth. It can therefore be argued that as the key underpinning conceptual tool mathematics enables the global disparities in wealth and life chances manifested in the human world. Mathematics, science and technology are used in the manufacture of guns, explosives, nuclear and biological weapons, battlefield computer systems, military drones and smart bombs, as well as tobacco products, and other potentially destructive artefacts and tools (Ernest 2018). Beyond these overt applications is the even more sinister invasion of social policy and life by mathematisation. People and social practices are replaced by metrics and social decision-making processes replaced by algorithms thus reconstructing personal and social life in involuntary ways to which no assent has been given. As metrics replace humans so too are levels of trust eroded, thus further degrading the social cohesion and affective structures of society. My argument here is not that we should oppose all of these applications of mathematics, nor neoliberalism, nor the western capitalist system overall from the outset. Rather it is that we should to acknowledge the implications of mathematics in all of its widespread and fundamental applications across society, many of which are invisible. We must educate students at all levels to see mathematics at work in describing, formatting and changing our world. Mathematics has a hidden dark side, its uses and applications in education and society have costs and harmful outcomes, as well as the more widely acknowledged benefits. Only when we acknowledge this dark side can we start to plan and act on ameliorating, reducing and countering the harm done, the algorithmic injustices. Hopefully, the ‘numeracy plus’ curriculum for all that I propose, taught with plenty of examples that raise ethical issues, will put mathematical tools for beginning to comprehend the uses and abuses of mathematics in society into the hands of a well informed critical citizenry. We need to prioritise the introduction of philosophical and especially ethical thinking in education at all levels (Ernest 2018). No mathematics should be taught that is not illustrated with ‘real world’ ethical dilemmas and problems. Mathematicians should not be trained merely as technical experts solely looking inwards. All professionals should be concerned with the ethics of their practices, as already happens in many cases such as with doctors, nurses, lawyers, scientists, police and military personnel. It is eye-opening to contrast the burgeoning social practice and philosophy of mathematising, measuring, calculating and computerising everything around us, including our selves, with the emergent biophilia movement (Kellert & Wilson 1995). Biophilia, the love of life, means caring for and valuing all living things from microbes to giant whales, from minute traces of mould to giant forests, all the way to the Earth itself. This love means caring for all life, including humans, as they are, in their given state, within their ecologies. Replacing living things by artificially imposed metrics and measures is antithetical to biophilia. From its perspective, it behoves us to respect and care for all beings and environments around us on their own terms. However, the urgent problem of how we and the Earth can survive with dignity (D'Ambrosio 2007), in the face of global warming and environmental degradation cannot be understood let alone solved without mathematics (Boylan & Coles 2017). Vital applications include measuring levels like world temperatures, deforestation, ice pack and glacier melting, animal survival rates, species extinctions, pollution levels and the modelling of likely and possible futures algorithmically. Without mathematics and measurement we would not understand the damage that we continue to inflict on the world and its inhabitants. Without measures of disparities in wealth and income by gender, race, social class and socio-economic status we cannot know the extent of social injustices. Measures of infant mortality, life expectancy, morbidity rates, disease and medical treatment survival rates are essential for the health of any nation. In tandem with using mathematics to help solve the urgent environment crises we also need to address education and public understanding. Curricula in all school subjects, and especially in mathematics and science, need to foster understanding of the environmental crisis and the actions needed to help solve it. This is not an optional extra, it is an outstanding ethical responsibility and necessity (Abtahi et al. 2017). So too is highlighting the world’s social injustices in terms of widespread poverty and the huge financial disparities both within and between countries. There is much work to do in promoting an ethical mathematics education, as well as ethical mathematical practices in the academy and in the wider world. The ethical problems faced by mathematics in education and society are huge, and the first obstacle is getting mathematicians to acknowledge them. It is time to introduce an Hippocratic oath for all mathematicians. References Abtahi, Y., G?tze, P. Steffensen, L. Hauge, K. H. and Barwell, B. (2017). Teaching Climate Change in Mathematics Classrooms: An Ethical Responsibility, The Philosophy of Mathematics Education Journal, No. 32. . Accessed 10 August 2019.Allchin, D. (2004). Should the Sociology of Science Be Rated X? Science Education, Vol. 88, No. 6; pp. 934-946.Bakan, J. (2004). The Corporation. London: Constable. BBC News (2013). 'Dangerous' financial products named, 15 March 2013. . Accessed 21 August 2018.Becker, H. (1963). Outsiders, Oxford: Free Press.Beer, D. (2016). Metric Power, London: Palgrave Macmillan.Berman, E. and Hirschman, D. (2018). The Sociology of Quantification: Where Are We Now? Contemporary Sociology, Vol. 47, No. 3; pp. 257 - 266.Bourdieu, P. (1986). The Forms of Capital. J. G. Richardson (Ed.). Handbook of Theory and Research for the Sociology of Education. New York: Greenwood press. pp. 241-258.Boylan, M. & Coles, A. (2017). Is Another Mathematics Education Possible? An Introduction To a Special Issue on Mathematics Education and the Living World: Responses to Ecological Crisis, The Philosophy of Mathematics Education Journal, No. 32. . Accessed 10 August 2019.Brown, W. (2015). Undoing the Demos: Neoliberalism’s Stealth Revolution. New York: Zone Books.Buerk, D. (1982). An experience with some able women who avoid mathematics. For the Learning of Mathematics. Vol. 3, No. 2; pp. 19-24.Buxton, L. (1981). Do you Panic about Maths? Coping with Maths Anxiety. London: Heinemann Educational Books.Cal?skan, K (2010). Market threads: how cotton farmers and traders create a global commodity. Princeton, New Jersey: Princeton University Press. D’Ambrosio, U. (2007). Peace, Social Justice and Ethnomathematics. The Montana Mathematics Enthusiast, Monograph 1, 2007; pp. 25-34.Davies, W. (2017). The Limits of Neoliberalism Authority, Sovereignty and the Logic of Competition. Thousand Oaks, California: SAGE Publications.De Mesquita, E. B. (2019). Economics After Neoliberalism - Quantification shapes how we think about public policy—often for the worse. Boston Review, Summer 2019 Issue. . Accessed 15 August 2019.EiM (no date). The Cambridge University Ethics in Mathematics Project. . Accessed 24 July 2019.Ernest, P. (1988). The Attitudes and Practices of Student Teachers of Primary School Mathematics, Proceedings of 12th International Psychology of Mathematics Education Conference, Veszprem, Hungary: OOK, Vol. 1; pp. 288-295.Ernest, P. (1991). The Philosophy of Mathematics Education. London: Routledge.Ernest, P. (2010) Why teach mathematics? Professional Educator, Vol. 9, No. 2 (June 2010) pp. 43-47. . Accessed 18 November 2019.Ernest, P. (2011). Mathematics and Special Educational Needs. Saarbrucken, Germany: Lambert Academic Publishing.Ernest, P. (2018). The Ethics of Mathematics: Is Mathematics Harmful?. In P. Ernest (Ed.). The Philosophy of Mathematics Education Today. Switzerland: Springer, 2018.Ernest, P. (in press). Mathematics, Ethics and Purism: An application of MacIntyre’s virtue theory. Forthcoming in Synthese, special issue on Virtue Theory of Mathematical Practices. Guest Editors: Andrew Aberdein, Colin Jakob Rittberg, Fenner Stanley Tanswell.Evans, J. (2000). Mathematical Thinking and Emotions in Context: Adults, Practices and Numeracy, London: Routledge.Fineman, S. (2004). Getting the Measure of Emotion - and the Cautionary Tale of Emotional Intelligence. Human Relations, Vol. 57; pp. 719-740.Foucault, M. (1976). Discipline and Punish, Harmondsworth: Penguin.Foucault, M. (1980). Power/Knowledge (edited by C. Gordon), New York: Pantheon Books.Gardner, H. (1983). Frames of Mind: The Theory of Multiple Intelligences. New York. Basic Books.Gorur, R. (2016). Seeing like PISA: A cautionary tale about the performativity of international assessments. European Educational Research Journal, Vol. 15, No. 5; pp. 598-616.Gould, S. J. (1981). The Mismeasure of Man. New York: W.W. Norton.Hayek, F. A. (1948). The use of knowledge in society. Individualism and the economic order. Chicago: Chicago University Press, pp. 77-91.Kellert, S. R. & Wilson, E. O., Eds., (1995) The Biophilia Hypothesis. Washington, DC, USA: Island Press - A Shearwater book.Kelman, H. C. (1973). Violence without moral restraint: reflections on the dehumanization of victims and victimizers. Journal of Social Issues, Vol. 29, No. 4; pp. 25-62. Lewis, M. (2019). Fit for purpose… Are we tracking our lives a fitbit too far. The Observer newspaper, UK. Sunday 10 November 2019, p. 50/Marjanovic, O., Cecez-Kecmanovic, D. & Vidgen, R. (2018). Algorithmic Pollution: Understanding and Responding to Negative Consequences of Algorithmic Decision-Making. U. Schultze, M. Aanestad, M. M?hring, C. ?sterlund, & K. Riemer, Eds. Living with Monsters? Social Implications of Algorithmic Phenomena, Hybrid Agency, and the Performativity of Technology. Switzerland: Springer, 2018; p 31-47.Maxwell, J. (1989). Mathephobia. P. Ernest, Ed., Mathematics Teaching: The State of the Art. London: Falmer Press; pp. 221-226.Mennicken, A. & Espeland, W. N. (2019). What’s New with Numbers? Sociological Approaches to the Study of Quantification. Annual Review of Sociology. Vol. 45, No. 24; pp. 1–23.Monbiot, G. (2017). Neoliberalism – the ideology at the root of all our problems. The Guardian, 15 April 2016. . Accessed 5 August 2019 (revised version).Mutodi, P and Ngirande, H. (2014). The Influence of Students` Perceptions on Mathematics Performance. Mediterranean Journal of Social Sciences, Vol. 5, No. 3; pp. 431-445.National Numeracy (2015) The debate about a ‘maths gene’. . Accessed 19 November 2019.O’Neil, C. (2016). Weapons of math destruction: How big date increase inequality and threatens democracy. New York, NY: Broadway books.Orwell, G. (1949). Nineteen Eighty-Four: A Novel. London: Secker & Warburg.Power, M. (1999). The Audit Society = Rituals of Verification. Oxford: Oxford University Press.Radical Statistics group (n. d.). About Us. . Accessed 3 August 2017.Raudenbush, S. W. (1984). Magnitude of teacher expectancy effects on pupil IQ as a function of the credibility of expectancy induction: A synthesis of findings from 18 experiments. Journal of Educational Psychology, Vol. 76, No. 1; pp. 85–97.Rosenthal, R. and Jacobson, L. (1968). Pygmalion in the Classroom. New York, USA: Holt, Rinehart and Winston.Russell, B., and Einstein, A. (1955). The Russell-Einstein Manifesto. . Accessed 23 April 2015.Sells, L. W. (1978). Mathematics - Critical Filter. The Science Teacher, 1978 (February); pp. 28-29.Sisk, V. F., Burgoyne, A. P., Sun, J., Butler, J. L., & Macnamara, B. N. (2018). To what extent and under which circumstances are growth mind-sets important to academic achievement? Two meta-analyses. Psychological Science, Vol. 29, No. 4; pp. 549-571.Skovsmose, O. and Ravn, O. (2019). Connecting Humans to Equations - A Reinterpretation of the Philosophy of Mathematics. Switzerland: Springer Nature.Skovsmose, O. Ed, (2014). Critique as Uncertainty. Charlotte, NC, USA: Information Age Publishing.von Mises, L. (1978). Epistemological Problems of Economics. New York, USA: New York University Press. (First published in German in 1933).West, J. (2012). Ethics and Quantitative Finance, Griffith Business School, Australia. from . Accessed 30 August 2018.Wikipedia (2019). Bildung. . Accessed 18 November 2019.Zevenbergen, R. (1998). Language, mathematics and social disadvantage: a Bourdieuian analysis of cultural capital in mathematics education. . Accessed 3 May 2015. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download